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Recent questions tagged determinant

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GATE DS&AI 2024 | Question: 25
Consider the $3 \times 3$ matrix $\boldsymbol{M}=\left[\begin{array}{lll}1 & 2 & 3 \\ 3 & 1 & 3 \\ 4 & 3 & 6\end{array}\right]$.The determinant of $\left(\boldsymbol{M}^{2}+12 \boldsymbol{M}\right)$ is $\_\_\_\_\_\_\_\_\_$.
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GATE CSE 2024 | Set 2 | Question: 37
Let $A$ be an $n \times n$ matrix over the set of all real numbers $\mathbb{R}$. Let $B$ be a matrix obtained from $A$ by swapping two rows. Which ... $A$ is zero, then the trace of $B$ is also zero
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Memory Based GATE DA 2024 | Question: 4
Consider the matrix\[\mathrm{M} = \begin{bmatrix}1 & 2 & 3 \\3 & 1 & 3 \\4 & 3 & 6\end{bmatrix}\]Find the value of \(|\mathrm{M}^2 + 12M|\).
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GO Classes CS/DA 2025 | Weekly Quiz 4 | Linear Algebra | Question: 7
Let $\mathrm{A}$ be a $3 \times 3$ matrix. Let $\mathbf{x}, \mathbf{y}, \mathbf{z}$ are linearly independent $3$-dimensional vectors. Suppose that we ... $\mathrm{A}$.
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GO Classes CS/DA 2025 | Weekly Quiz 4 | Linear Algebra | Question: 12
If $P=\left[\begin{array}{lll}1 & \alpha & 3 \\ 1 & 3 & 3 \\ 2 & 4 & 4\end{array}\right]$ is the adjoint of a $3 \times 3$ matrix $\mathrm{A},$ and $\operatorname{det(A)}=4,$ then $\alpha$ equals to?
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GO Classes CS/DA 2025 | Weekly Quiz 4 | Linear Algebra | Question: 13
Given the following matrix:$A=\left[\begin{array}{lll}1 & 2 & 2 \\2 & 1 & 2 \\2 & 2 & 1\end{array}\right]$ ... $I$ is true.Only II is true.Both I and II are true.Neither I, nor II are true.
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GO Classes CS/DA 2025 | Weekly Quiz 4 | Linear Algebra | Question: 15
Suppose $\mathbf{A}=\mathbf{B C}$, where $\mathbf{B}$ is a $4 \times 2$ matrix and $\mathbf{C}$ is a $2 \times 4$ matrix. Is $\mathbf{A}$ invertible? ... not invertible.Depends on $\mathbf{C}$ only.Depends on $\mathbf{B}$ and $\mathbf{C}$.
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GATE CSE 2023 | Question: 8
Let\[A=\left[\begin{array}{llll}1 & 2 & 3 & 4 \\4 & 1 & 2 & 3 \\3 & 4 & 1 & 2 \\2 & 3 & 4 & 1\end{array}\right]\]and\[B=\left[ ... $\operatorname{det}(A B)=\operatorname{det}(A)+\operatorname{det}(B)$
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GATE CSE 2023 | Memory Based Question: 13
Let$A=\left[\begin{array}{llll}1 & 2 & 3 & 4 \\4 & 1 & 2 & 3 \\3 & 4 & 1 & 2 \\2 & 3 & 4 & 1\end{array}\right]$ ... {det} \mathrm{B}=-\operatorname{det} \mathrm{A}$\operatorname{det} \mathrm{A}=\operatorname{det} \mathrm{B}$
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Self doubt.
If A, B & C are matrices & AB=AC then B=C?as we know it is not always true because when A is singular matrix then B=C not possible so what is the right ans to ... C is (always not equal) or (may or may not be equal) or (simply not equal)?
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TIFR CSE 2022 | Part A | Question: 4
Consider the polynomial $p(x)=x^3-x^2+x-1$. How many symmetric matrices with integer entries are there whose characteristic polynomial is $p$? (Recall that the ... I)$ where $I$ is the identity matrix.)$0$1$2$4$Infinitely many
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Best Open Video Playlist for Determinants Topic | Linear Algebra
Please list out the best free available video playlist for Determinants Topic from Linear Algebra as an answer here (only one playlist per answer). We'll then ... to be selected as best.For the full list of selected videos please see here
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GO Classes Test Series 2023 | Linear Algebra | Test | Question: 9
Compute the determinant of$A=\left[\begin{array}{cccc}1 & -1 & 0 & 3\\2 & 5 & 2 & 6\\0 & 1 & 0 & 0\\1 & 4 & 2 & 1\end{array}\right].$
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Applied Grand Test 2
What is the value of the given determinant ?
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3 votes
Applied Test Series
What is the value of the determinant ?
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